In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all directions. Assuming that the polluted area is circular, determine how fast the area is increasing when the radius of the circle is 60 ft and is increasing at the rate of 1 2 ft/sec?

2260.8 ft ^ 2 / s

Step-by-step explanation:

To solve the problem we first know that:

dr / dt = 6 ft / s

r = 60 ft

Now they ask us for dA / dt, the change of the area with respect to time, by chain rule we have to:

dA / dt = dA / dr * dr / dt

we have that A = pi * r ^ 2

d (pi * r ^ 2) / dr

deriving the above we are left with:

 2 * pi * r

replacing:

dA / dt = (2 * pi * r) * 6

dA / dt = 2 * 3.14 * 60 * 6

dA / dt = 2260.8 ft ^ 2 / s

therefore the area change per second is 2260.8 ft ^ 2 / s

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i

hello i am doing good for you that it's summer in your country or state ; )

btw in my country we just have sun and rain as (because i live in the caribbean lol)

also, thx a lot for the points : )